Vibrational mechanisms of admixture transport in convective systems

Abstract

The equations of vibrational convection for non-uniform molecular fluid mixtures have been derived when the diffusion coefficient depends on concentration of components. Equation system is received with the help of the averaging method in the limiting case of high frequencies and small values of amplitude. In a definite sense this one is identical mathematically to well-known equations system of thermal vibrational convection in an approximation of Zen’kovskaya and Simonenko. The problem of concentration field evolution in a plane infinite fluid layer has been solved numerically by the method of finite differences. The modeling situation with homogeneous one-dimensional source distribution of a heavy component on the solid boundary was considered. It was found that the high frequency vibrations can induce mean convective flow in a cavity even in the absence of a temperature inhomogeneity and in the case of weightlessness. At the same time vibrations cause the flow in the form of rolls which occupy the whole volume. The process of admixture ablation into the fluid has been considered for arbitrary oriented vibrations. It has been shown that in dependence on the direction of the vibration axes the process of admixture redistribution passes with various rates. First of all it is determined by the intensity degree of the averaged vibrational flow in a fluid. The modeling calculations were carried out for different values of the non-dimensional parameter which describes the dependence of diffusion coefficient on concentration. Numerical simulation demonstrates that most strong effect of admixture ablation takes place for longitudinal vibrations. On the other hand vibrations which are transversal to layer damps averaged flow. In this case the mass transfer has diffusive character. Also the dependence of mass transfer on diffusion coefficient is most pronounced for tangential vibrations.Received 27.07.2016; accepted 18.08.2016